Groups and Dynamics Seminar

Date: January 25, 2023

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Nataliya Goncharuk, Texas A&M University

Title: Renormalization operators and Arnold tongues

Abstract: Many studies in circle dynamics are devoted to rotation numbers of circle maps, and to so-called Arnold tongues: level sets of rotation numbers in parametric families of circle maps. In particular, E.Risler proved in 1999 that irrational (Diophantine) Arnold tongues in analytic families of circle diffeomorphisms are analytic. In contrast to this result, Llave and Luque observed in 2011 using numerical investigations that Arnold tongues are only finitely smooth near critical circle maps. With M.Yampolsky, we provided explanations of these effects in terms of renormalization operators.